Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

17. What is the solution, if any, of the equation

2 / (x + 3) - 3 / (4 - x) = (2x - 2) / (x² - x - 12)

(1) -1

Follow along with the image below.
Because x² - x - 12 is the product of (x + 3)(x - 4), we can multiply the entire equation by (x + 3)(x - 4).
To get (x - 4) in the denominator of the middle fraction, multiply the top and bottom of the fraction by -1.
Multiplying removes all the denominators and sets up an equation that solved in a couple of steps.
The solution is x = -1.

Because it was multiple choice, you could also use the graphing calculator to solve the problem:
As shown below, put the left side of the equation into y₁ and the right side into y₂ and graph.
Check the values for -1 and -5. You can see that -1 has the same values but -5 does not. Likewise, all real numbers and no real solutions are obviously incorrect.

18. In 2013, approximately 1.6 million students took the Critical Reading portion of the SAT exam. The mean score, the modal score, and the standard deviation were calculated to be 496, 430, and 115, respectively.
Which interval reflects 95% of the Critical Reading scores?

(4) 496 + 230

The standard deviation uses the mean, which is 496 in this example. About 95% of the data falls within TWO standard deviations from the mean. Double 115 and you get 230.




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